If 3x + 2 = 0 (mod 7), which of the following values can x assume? O a. O b. 0 O c. -1 O d. -3 2.

Q: What is the value of ((131)39 + 11 ⋅ (-11))mod13 ? a. 3 b. 9 c. 10 d. 23

A: Solution

Q: Find the 5-1 mod 57 A) 4 B) 11 C) 12 D) 23

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Q: b"=1 (mod n) is valid for which of the following pair (b,n) (9.7,1729) (97,1729) (-97,1729)…

A: Answer

Q: What is the value of Y after solving the following expression? Y= Not 15 Mod 5 = 24/6 And 50 / 2 >=…

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Q: . If 4x - 3 = 19 (mod 31), then the value of x (mod 31) is O 26 О 18 D 21 D 30

A: Arithmetic modulo

Q: Given: x = -30 (mod 12) Which of the following integers are valid solutions for x? A)   -18 B)…

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Q: If today is Thursday, what day of the week will it be 20 days from now? Friday O Monday O Thursday O…

A: Introduction: For two given integers a and n, either n divides a or n doesn't divide a. When, n…

Q: The value of 52003 mod 7 is? 4 0 3 0 9 O 8 0

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Q: b=3(mod19)

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Q: For each of the following statements, use the definition of congruence to show why the statement is…

A: Since you have posted multiple sub parts question but we can solve only first three sub parts of the…

Q: Number theory

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Q: (c) For each integer a, if a 4 (mod 8), then a 2 (mod 8).

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Q: For the given values of n=7 and a=30, find the number b∈{0,1,…,n−1} for which a≡b(modn).

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Q: If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b3 c (тod n) (b) b2 =…

A: Given below the detailed solution

Q: (1) Consider the equation 2.x +1 = 0 mod n. For which n are there no solutions? one solution?…

A: Congruence

Q: QUESTION 4 Consider the congruence x 4 (mod 5) Then, x equal to: O a. 4 O b. -1 O c. 9 O d. all…

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Q: 16. Which of the following congruencies has NO solution? . A. 24x = 18(mod 39) B. 5x = 4(mod 10) C.…

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Q: (a) (b) (c) (d) If P and Q are odd positive integers, we have mn ( ² ) ( ² ) = (m²). m Ⓒ) (@) = (₂)…

A: Since you have asked a question with multiple subparts , we will solve first three subparts for you.…

Q: One of the foll owing is not true: Oa 0= 10 mod 5 b None Oc 14=2 mod 6 Od 20 =0 mod 5 Oe -24 mod 6

A: Here we use rules of modular operation.

Q: Which of the following is true? a. 24 = 3 (mod4) b. 56= 4(mod5) c. 62 = 4(mod4) d. 58 = 3 (mod5) Oa…

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Q: 4. The statement P-> Q is equivalent to -PA Q. 5. To prove the statement: If ab = 0 then a = 0 or b…

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Q: What is the inverse of (show the steps) a) 20 mod 49 b) 7 mod 26

A: Multipart :  We have , 20 mod 49 We need to find Inverse. We know that , if aa¯ ≡ 1 mod m then a¯ is…

Q: The solution for xr° =10(mod11) is a) 5 b) 6 c) No solution d) 4 Answer A D Submit

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Q: Consider: for any integers a and b, if (a3 + b3) mod 3 does not equal 0, then (a + b) mod 3 does not…

A: The contrapositive of A implies B is not B implies not A. We use this and solve this problem.…

Q: The value of 14723 (mod 153) is A) 67 B) 52 C) 54 D) 73

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Q: One of the following is a solution of 306x = 90 (mod 360) 107 has no solution 105 106 108

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Q: The expression 13 (mod 6) is congruent    A. 1 B. 2 C. 3 D. 4

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Q: If 3x + 2 = 0 (mod 7), which of the following values can x assume? О а. -3 O b. 0 О с. 2 O d. -1

A: Given 3x + 2 = 0 (mod 7).

Q: Solve each equation for x. (If there is no solution, enter NO SOLUTION.) (a)     x + 8 ≡ 1, (mod 9)…

A: We solve each equation for x.

Q: For each of the following pairs, determine whether they are congruent modulo (b) 132 and 10 11.…

A: Given below the detailed solution

Q: If x00 = 1(mod 109) then possible value of x is a) 108 (b) 218 (c) 109 (d) None of these

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Q: Ti If a = b (mod n) and b =c (mod n) then which of the following is true. (a) a = c (mod n) (b) a2 =…

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Q: The inverse of 5 mod 10 а. 5 b. 2 Ос. 10 O d. The inverse does not exist

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Q: Given 3 * 4.52 = x(mod 53), Here x is equal

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the value of x if any. Show your complete solution. 1.   (13 + x) = 3 mod 16 x = 2.   (3x +…

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Q: Perform the indicated operations. a.) 3 + 40, (mod 5)      __________________ , (mod 5) b.) 5 − 8,…

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Q: One of the following is a solution of 81x = 54 (mod 108) 43 47 45 42 has no solution

A: We are given the Equation :

Q: the given values of n=9 and a=69, find the number b∈{0,1,…,n−1} for which a≡b(mod n

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Q: If a = b (mod n) and b = c (mod n) then which of the following is true. (a) a = c (mod n) (b) a? =…

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Q: Which of the following is not a possible value for y ≡≡ 17 mod 8 in the equation ? Group of answer…

A: Consider the given equation.

Q: (a) For each integer a, if a? = 1 (mod 10), then a = 1 (mod 10). (b) Let a, b, and c be integers. If…

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Q: Which of the following is false? a. (x-y+2) = (x-y-11) (mod13) b. (x-y+2) = (x-y-32) (mod 17) c.…

A: Sol:- Check each statement:- a.x-y+2≅x-y-11mod 13Since, 2 mod 13 = -11 , This statement is…

Q: "Given: x = -30 (mod 12) Which of the following integers are valid solutions for x 18- O 30 20 36-

A: Solution:- -30mod(12) To obtain -30mod12 conduct these three steps:

Q: 2. Let A = {n? + n € Z :n € Z} and B = {r € Z : r³ – 32³ + 2x = 0 mod 5}. Prove or disprove: A B.…

A: That's easy, just needs a little congruence. Have a great day!!!

Q: QUESTION 4 Consider the congruence x 4 (mod 5) Then, x equal to: O a. 4 O b.-1 OC 9 Od. all options…

A: We have to find x

Q: Which of the following values makes the expression un (x – 3) (x + 3) y = (x – 7) (x + 3) | O x= -7…

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Q: Which one of the following is correct? a. 30 3 (mod 5) O b. 25 3 (mod 4) Oc. 31 3 (mod 7) O d. 20 3…

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Q: State whether the following numbers are rational or irrational. a) V4+7/2 b) 36 c) V11²510716 State…

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Q: If 3(26!) = x(mod29), then x = None of the choices O 11 13 15

A: The given problem is to solve the given congruence equation. 3(26!)= x (mod 29).

Q: 1)For each of the following, find an integer value x which satisfies the equation, or explain why…

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